Let's see, what is the original question? The poster thinks that taking a knight with a bishop should be good if it results in the opponent getting doubled pawns. And the poster also specifically asks about bishop takes knight. I will address both parts of the question.
Of course, everything depends on the position. So it is difficult to give a general answer. However, I shall try. But keep in mind that chess does not have a general solution, only heuristics to go by. And sometimes they fail.
Presumably because we "know" that doubled pawns are bad. However, this does not have to be the case. As the poster already found out, because in the given example sometimes people play Bxc6, but they also play Ba4.
It is all about control.
Pawns are the strongest when they are next to each other, in line. Like in the starting position. Why? They control all squares one row in front of them. Every pawn you move also creates some weakness. If I move my pawn from b2 to b3, the a3-square is weakened, because no pawn can defend it.
Disadvantages of doubled pawns:
- the pawn that captured now controls different squares than before
- if the doubled pawns are isolated, they are really weak. The opponent can put a piece in front of the doubled pawns that can never be chased away by a pawn (same holds when the neighbouring pawn is already ahead: if Black plays b7-b5 in the example structure, the square c5 is very weak
- they are in each other's way, so they move slower
Advantages of doubled pawns:
- They control a lot of consequent squares. In the example they control b6, b5, d6 and d5.
- A doubled pawn means a (semi-)open file. Which can be good for your rook.
- A doubled pawn means a diagonal has been opened (like in the example: the c8-bishop now can be developed)
All in all, doubled pawns are good for defending, but not for attacking.
Bishop takes knight
The value of a bishop or knight depends on the position, of course. Roughly it can be said they are about equal strength. But they have different advantages.
A knight can jump over pieces, so it is a great blockading piece. And it is strong in closed positions. Also, it can reach any square of the board. However, a knight is a slow-moving piece. For instance, it takes several (six) moves to go from a1 to h8.
A bishop can make long moves. For instance, it takes only one move to go from a1 to h8. This means it works best in open (many diagonals) positions. However, it can only reach half of the squares. And if the bishop is blocked by a pawn chain, it can be passive and bad.
However, the pair of bishops is considered to be a real asset. You have the advantages of the bishop, but not the disadvantage of only controlling half of the squares. Also, it is up to you to decide when to give up the bishop pair and convert to some other advantage.
Back to the example
To come back to the example: the move Bxc6 hands the bishop pair to Black. Since this is very early in the game, Black can handle accordingly and play with the two bishops (and try to open up the game). And the doubled pawns are not that weak.
Another example of doubled pawns, where the bishop does take the knight is in the Nimzo-Indian defence. After
1.d4 Nf6 2.c4 e6 3.Nc3 Bb4 4.a3 Bxc3+ 5.bxc3
These doubled pawns are a little bit different than the ones from the Ruy Lopez example. The most important detail: the c4-square is weak. No pawn can control it. A strategy for Black is to play against this pawn by playing d6, e5, c5, b6, Nc6-a5 end Ba6. But that is something for another time...